. Tab, C.3 ? Etudes d'intérêt et perspectives Etudes d'intérêt et perspectives Références Fractal

C. Condemine, N. Delorme, J. Soen, J. Durupt, J. P. Blanc et al., Besancon- Voda, A 0.8ma 50hz 15 bits sndr ?? closed-loop 10g accelerometer using an 8 th -order digital compensator, ISSCC'05 -The, IEEE International on Solid-State Circuits Conference - Digest of Technical Papers, pp.248-249, 2005.

M. Pelissier, D. Morche, and J. Soen, A new pulse detector based on super-regeneration for UWB low power applications, 2006 IEEE International Conference on Ultra-Wideband, 2006.
DOI : 10.1109/ICU.2006.281623

J. Soen, A. Voda, and C. Condemine, Controller design for a closed-loop micromachined accelerometer, Control Engineering Practice, vol.15, issue.1, pp.57-68, 2005.
DOI : 10.1016/j.conengprac.2006.03.001
URL : https://hal.archives-ouvertes.fr/hal-00375822

M. Elwenspoek and R. Wiegerink, Mechanical microsensors, 2001.
DOI : 10.1007/978-3-662-04321-9

R. Y. Chiang and M. G. Safonov, Robust control toolbox -user's guide, The MathWorks, 1998.

J. C. Doyle, K. Glover, P. Khargonekar, and B. Francis, State-space solutions to standard H/sub 2/ and H/sub infinity / control problems, IEEE Transactions on Automatic Control, vol.34, issue.8, pp.831-847, 1989.
DOI : 10.1109/9.29425

P. V. Gade, Performance enhancement and stability robustness of wing/store flutter suppression system, 1998.

R. E. Kalman, A New Approach to Linear Filtering and Prediction Problems, Journal of Basic Engineering, vol.82, issue.1, pp.35-45, 1960.
DOI : 10.1115/1.3662552

I. D. Landau, R. Lozano, and M. M. Saad, Adaptive control, 1997.
URL : https://hal.archives-ouvertes.fr/hal-01060308

L. Ioan-doré, Commande des systèmes -conception, identification et mise en oeuvre, 2002.

A. J. Laub, M. T. Heath, C. C. Paige, and R. C. Ward, Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms, IEEE Transactions on Automatic Control, vol.32, issue.2, pp.115-122, 1987.
DOI : 10.1109/TAC.1987.1104549

L. Ljung and N. J. , System Identification -Theory for the User, 1999.

L. Ljung and T. Glad, Modeling of dynamic systems, N.J, 1994.

W. M. Lu, K. Zhou, and J. C. Doyle, Stabilisation of uncertain linear systems : An LFT approach, IEEE Transactions on Automatic Control, vol.41, issue.1, 1996.

B. Moore, Principal component analysis in linear systems: Controllability, observability, and model reduction, IEEE Transactions on Automatic Control, vol.26, issue.1, pp.17-31, 1981.
DOI : 10.1109/TAC.1981.1102568

R. Pintelon and J. Schoukens, System identification : A frequency domain approach, no, 2001.
DOI : 10.1002/9781118287422

D. Simon, Optimal state estimation : Kalman, H ? , and nonlinear approaches, 2006.
DOI : 10.1002/0470045345

S. Skogestad and I. Postlethwaite, Multivariable feedback control : Analysis and design, 2005.

T. Söderström and P. Stoica, System Identification, Journal of Dynamic Systems, Measurement, and Control, vol.115, issue.4, 1989.
DOI : 10.1115/1.2899207

R. F. Stengel, Optimal control and estimation, 1994.

K. Zhou, J. Doyle, and K. Glover, Robust and optimal control Nonresonant micromachined gyroscopes with structural modedecoupling, IEEE Sensors Journal, vol.3, issue.4, pp.497-506, 1995.

B. E. Boser and R. T. Howe, Surface micromachined accelerometers, IEEE Journal of Solid-State Circuits, vol.31, issue.3, pp.366-375, 1996.
DOI : 10.1109/4.494198

E. Colinet, Nouvelles architectures et méthodes de conception de microsystèmes ?? et de microsystèmes résonants, 2005.

E. Colinet, J. Juillard, S. Guessab, and R. Kielbasa, Resolution enhancement of a sigmadelta micro-accelerometer using signal prediction, Proceedings of the 2004 International Conference on MEMS, NANO and Smart Systems, pp.409-413, 2004.

C. Condemine, ContributionsàContributions`Contributionsà la conception de microsystèmes sigma-delta asservis, 2001.

N. Delorme, M. Belleville, and J. Chilo, Inductance and capacitance analytic formulas for VLSI interconnects, Electronics Letters, vol.32, issue.11, pp.996-997, 1996.
DOI : 10.1049/el:19960689

Y. Dong, M. Kraft, C. Gollasch, and W. Redman-white, A high-performance accelerometer with a fifth-order sigma???delta modulator, Journal of Micromechanics and Microengineering, vol.15, issue.7, pp.22-29, 2005.
DOI : 10.1088/0960-1317/15/7/004

A. Fargamarqù-es, R. Castelì-o-costa, and A. M. Shkel, Modelling the electrostatic actuation of MEMS : state of the art, 2005.

T. B. Gabrielson, Mechanical-thermal noise in micromachined acoustic and vibration sensors, IEEE Transactions on Electron Devices, vol.40, issue.5, pp.903-909, 1993.
DOI : 10.1109/16.210197

R. K. Gupta and S. D. Senturia, Pull-in time dynamics as a measure of absolute pressure, Proceedings IEEE The Tenth Annual International Workshop on Micro Electro Mechanical Systems. An Investigation of Micro Structures, Sensors, Actuators, Machines and Robots, pp.290-294, 1997.
DOI : 10.1109/MEMSYS.1997.581830

M. Handtmann, Dynamische regelung mikroelektromechanischer systeme (mems) mit hilfe kapazitiver signalwandlung und kraftrückkoppelung, 2004.

M. Handtmann, R. Aigner, A. Meckes, and G. K. Wachutka, Sensitivity enhancement of mems inertial sensors using negative springs and active control, Sensors and Actuators A, pp.97-98, 2002.

R. Houlihan and M. Kraft, Modelling squeeze film effects in a MEMS accelerometer with a levitated proof mass, Journal of Micromechanics and Microengineering, vol.15, issue.5, pp.893-902, 2005.
DOI : 10.1088/0960-1317/15/5/001

X. Jiang, Capacitive position-sensing interface for micromachined inertial sensors, 2003.

V. Kaajakari, Pull-in voltage in electrostatic microactuators

T. Kajita, U. K. Moon, and G. C. Temes, A noise shaping accelerometer interface cicuit for two-chip implementation, IEEE Instrumentation and Measurement Technology Conference, pp.1581-1586, 2001.

M. Kraft, Closed-loop digital accelerometer employing oversampling conversion, 1997.

H. Kulah, J. Chae, N. Yazdi, and K. Najafi, Noise Analysis and Characterization of a Sigma-Delta Capacitive Microaccelerometer, IEEE Journal of Solid-State Circuits, vol.41, issue.2, pp.352-361, 2006.
DOI : 10.1109/JSSC.2005.863148

H. Kulah and K. Najafi, A low noise switched-capacitor interface circuit for sub-micro gravity resolution micromachined accelerometers, ESSCIRC, 2002.

T. A. Lauderdale and O. M. O-'reilly, Modeling MEMS resonators with rod-like components accounting for anisotropy, temperature, and strain dependencies, International Journal of Solids and Structures, vol.42, issue.26, pp.6523-6549, 2005.
DOI : 10.1016/j.ijsolstr.2005.06.010

M. A. Lemkin, Micro accelerometer design with digital feedback control, 1997.

C. H. Liu and T. W. Kenny, A high-precision, wide-bandwidth micromachined tunneling accelerometer, Journa of MicroElectroMechanical Systems, vol.10, issue.3, pp.425-433, 2001.

C. H. Liu, H. K. Rockstad, and T. W. Kenny, Robust controller design via µ-synthesis for high-performance micromachined tunneling accelerometer, Proceedings of the 1999 American Control Conference, pp.247-252, 1999.

. Roukes, Intrinsic dissipation in high-frequency micromechanical resonators, Physical Review B (Condensed Matter and Materials Physics), vol.66, issue.8, pp.85416-85431, 2002.

M. Napoli, B. Bamieh, and K. L. Turner, A Capacitive Microcantilever: Modelling, Validation, and Estimation Using Current Measurements, Journal of Dynamic Systems, Measurement, and Control, vol.126, issue.2, pp.319-326, 2004.
DOI : 10.1115/1.1767851

M. Napoli, C. Olroyd, K. L. Turner, and B. Bamieh, A novel observer based sensing scheme for the displacement of electrostatically actuated microcantilevers, Proceedings of IEEE Sensors, 2004., pp.24-27, 2004.
DOI : 10.1109/ICSENS.2004.1426402

C. T. Nguyen, Micromechanical signal processor, 1994.

S. R. Norsworthy, R. Schreier, and G. C. Temes, Delta-sigma data converters : Theory, design and simulation, 1996.
DOI : 10.1109/9780470544358

A. Tesfaye, H. S. Lee, and M. Tomizuka, A sensitivity optimization approach to design of a disturbance observer in digital motion control systems, IEEE/ASME Transactions on Mechatronics, vol.5, issue.1, pp.32-38, 2000.
DOI : 10.1109/3516.828587

M. Tomizuka and C. C. Wang, Design of robustly stable disturbance observers based on closed-loop consideration using H ? optimization and its applications to motion control systems, Proceeding of the 2004 American Control Conference, pp.3764-3769, 2004.

F. M. White, Viscous fluid flow, 1991.

L. Yao, M. Steyaert, and W. Sansen, 1V 88dB 20kHz modulator in 90nm CMOS, ISSC Digest of tehchincal papers, pp.80-81, 2004.

E. M. Abdel-rahman, A. H. Nayfeh, and M. I. Younis, Dynamics of an electrically actuated resonant microsensor, Proceedings International Conference on MEMS, NANO and Smart Systems, 2003.
DOI : 10.1109/ICMENS.2003.1221991

J. S. Aldridge and A. N. Cleland, Noise-enabled precision measurements of a duffing nanomechanical resonator, Physical review letters 94, pp.1-4, 2005.

R. Almog, S. Zaitec, and E. Buks, High intermodulation gain in a micromechanical duffing resonator, arXiv :con-mat, pp.1-3, 2005.

R. Baskaran and K. L. Turner, Mechanical domain coupled mode parametric resonance and amplification in a torsional mode micro electro mechanical oscillator, Journal of Micromechanics and Microengineering, vol.13, issue.5, pp.701-707, 2003.
DOI : 10.1088/0960-1317/13/5/323

C. Cruz-hernández and H. Serrano-guerrero, Cryptosystems based on synchronized Chua's circuits, 16th IFAC World Congress, 2005.

T. L. Daniel and M. S. Tu, Animal movement, mechanical tuning and coupled systems, The Journal of Experimental Biology, vol.202, pp.3415-3421, 1999.

F. Davide, M. Andersson, M. Holmberg, and I. Lundström, Chaotic chemical sensing, IEEE Sensors Journal, vol.2, issue.6, pp.656-662, 2002.
DOI : 10.1109/JSEN.2002.807771

G. Duffing, Erzwungene schwingungen bei veränderlicher eigenfrequenz und ihre techniche bedeutung, 1918.

V. M. Eguiluz, Y. Ospeck, A. J. Hudspeth, and M. O. Magnasco, Essential Nonlinearities in Hearing, Essential nonlinearities in hearing, pp.5232-5235, 2000.
DOI : 10.1103/PhysRevLett.84.5232

F. Filhol, E. Defa¨ydefa¨y, C. Divoux, C. Zinck, and M. T. Delaye, Resonant micro-mirror excited by a thin-film piezoelectric actuator for fast optical beam scanning, Sensors and Actuators A : Physical, pp.123-124, 2005.

G. M. Gale, F. Hache, and M. Cavallari, Broad-bandwidth parametric amplification in the visible : femtosecond experiments and simulations, Selected Topics in Quantum Electronics, IEEE Journal, vol.4, issue.2, pp.224-229, 1998.

D. S. Greywall, B. Yurke, P. A. Busch, A. N. Pargellis, and R. L. Willet, Evading amplifier noise in nonlinear oscillators, Physical Review Letters, vol.72, issue.19, pp.2992-2995, 1994.
DOI : 10.1103/PhysRevLett.72.2992

A. Husain, J. Hone, H. W. Ch, X. M. Postma, T. Huang et al., Nanowire-based very-high-frequency electromechanical resonator, Applied Physics Letters, vol.83, issue.6, pp.1240-1242, 2003.
DOI : 10.1063/1.1601311

A. Kern and R. Stoop, Nonlinear dynamics of cochlear information processing, NDES, pp.190-193, 2004.

S. Krylov, I. Harari, and Y. Cohen, Stabilization of electrostatically actuated microstructures using parametric excitation, Journal of Micromechanics and Microengineering, vol.15, issue.6, pp.1188-1204, 2005.
DOI : 10.1088/0960-1317/15/6/009

S. Lee and C. T. Nguyen, Influence of automatic level control on micromechanical resonator oscillator phase noise, IEEE International Frequency Control Symposium and PDA Exhibition, jointly with the 17 th European Frequency and Time Forum, pp.341-349, 2003.

R. Lifshitz and M. C. Cross, Response of parametrically driven nonlinear coupled oscillators with application to micromechanical and nanomechanical resonator arrays, Physical Review B, vol.67, issue.13, pp.134302-134314, 2003.
DOI : 10.1103/PhysRevB.67.134302

N. Mahmoudian, M. R. Aagaah, G. N. Jazar, and M. Mahinfalah, Dynamics of a Micro Electro Mechanical System (mems, International Conference on MEMS, NANO and Smart Systems, 2004.

S. Mojon, Using nonlinear oscillators to control the locomotion of a simulated biped robot, Master's thesis, EPFL -BIRG, 2004.

L. Moreau, E. Sontag, and M. Arcak, Feedback tuning of bifurcations, Systems & Control Letters, vol.50, issue.3, pp.229-239, 2003.
DOI : 10.1016/S0167-6911(03)00157-9

L. Moreau and E. D. Sontag, Balancing at the border of instability, Physical Review E, vol.68, issue.2, pp.1-4, 2003.
DOI : 10.1103/PhysRevE.68.020901

K. Murali, S. Sinha, and I. R. Mohamed, Chaos computing: experimental realization of NOR gate using a simple chaotic circuit, Physics Letters A, vol.339, issue.1-2, pp.39-44, 2005.
DOI : 10.1016/j.physleta.2005.02.044

M. Napoli, R. Baskaran, K. L. Turner, and B. Bamieh, Understanding mechanical domain parametric resonance in microcantilevers, The Sixteenth Annual International Conference on Micro Electro Mechanical Systems, 2003. MEMS-03 Kyoto. IEEE, pp.169-172, 2003.
DOI : 10.1109/MEMSYS.2003.1189713

M. Napoli, Z. Wenhua, K. L. Turner, and B. Bamieh, Characterization of electrostatically coupled microcantilevers, Microelectromechanical Systems, pp.14-295, 2005.

A. H. Nayfeh and M. I. Younis, Dynamics of MEMS resonators under superharmonic and subharmonic excitations, Journal of Micromechanics and Microengineering, vol.15, issue.10, pp.1840-1847, 2005.
DOI : 10.1088/0960-1317/15/10/008

A. and H. Nayfeh, Introduction to perturbation techniques, 1993.

C. T. Nguyen, Micromechanical signal processor, 1994.

C. T. Nguyen and R. T. Howe, An integrated CMOS micromechanical resonator high-Q oscillator, IEEE Journal of Solid-State Circuits, vol.34, issue.4, pp.440-455, 1999.
DOI : 10.1109/4.753677

L. M. Pecora, T. L. Carroll, G. A. Johnson, and D. J. Mar, Fundamentals of synchronization in chaotic systems, concepts, and applications, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.7, issue.4, pp.520-541, 1997.
DOI : 10.1063/1.166278

H. W. Ch-postma, I. Kozinsky, A. Husain, and M. L. Roukes, Dynamic range of nanotube- and nanowire-based electromechanical systems, Applied Physics Letters, vol.86, issue.22, pp.223105-223108, 2005.
DOI : 10.1063/1.1929098

J. F. Rhoads, S. W. Shaw, K. L. Turner, and R. Baskaran, Tunable mems filters that exploit parametric resonance, To appear in the, Journal of Vibration and Acoustics, pp.1-19, 2005.

J. F. Rhoads, S. W. Shaw, K. L. Turner, J. Moehlis, B. E. Demartini et al., Nonlinear Response of Parametrically-Excited MEMS, Volume 1: 20th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C, 2005.
DOI : 10.1115/DETC2005-84603

D. Rugar and P. Grütter, Mechanical parametric amplification and thermomechanical noise squeezing, Physical Review Letters, vol.67, issue.6, pp.699-702, 1991.
DOI : 10.1103/PhysRevLett.67.699

S. W. Shaw, J. F. Rhoads, and K. L. Turner, Parametrically excited mems oscillators with filtering applications, 10 th Conference on Nonlinear Vibrations, Stability, and Dynamics of Structures, 2004.

C. P. Silva, Introduction to chaos and its potential applications (slides), IEEE IMS Workshop, 2003.

M. I. Sobhy and A. R. Shehata, Chaotic algorithms for data encryption, methods of attack and counter measures, IEEE IMS Workshop, 2003.

E. D. Sontag, Some new directions in control theory inspired by systems biology, Systems Biology, vol.1, issue.1, pp.9-18, 2004.
DOI : 10.1049/sb:20045006

R. Stoop, Auditory two-tone suppression from a subcritical Hopf cochlea, Physica A: Statistical Mechanics and its Applications, vol.351, issue.1, pp.175-183, 2005.
DOI : 10.1016/j.physa.2004.12.019

K. L. Turner, R. Baskaran, and Z. Wenhua, Using nonlinear dynamics for performance enhancement in resonant micro and nano-scale devices, Decision and Control, Proceedings . 42nd IEEE Conference on, pp.2650-2651, 2003.

G. Wang, D. Chen, J. Lin, and X. Chen, The application of chaotic oscillators to weak signal detection, IEEE Transactions on Industrial Electronics, vol.46, issue.2, pp.440-444, 1999.
DOI : 10.1109/41.753783

C. Williams, Efficient chaotic communications over radio channels -slides, Non-linear Dynamics and Bifurcations Workshop, 2003.

M. I. Younis, Modeling and simulation of microelectromechanical systems in multi-physics fields, 2004.

M. I. Younis, E. M. Abdel-rahman, and A. H. Nayfeh, A reduced-order model for electrically actuated microbeam-based MEMS, Journal of Microelectromechanical Systems, vol.12, issue.5, pp.672-680, 2003.
DOI : 10.1109/JMEMS.2003.818069

B. Yurke, D. Greywall, A. N. Pargellis, and P. A. Busch, Theory of amplifier-noise evasion in an oscillator employing a nonlinear resonator, Physical Review A, vol.51, issue.5, pp.4211-4229, 1995.
DOI : 10.1103/PhysRevA.51.4211

W. Zhang, R. Baskaran, and L. T. Kimberly, Nonlinear behavior of a parametric resonancebased mass sensor, Proceedings of IMECE 2002, pp.1-5, 2002.

W. Zhang and K. L. Turner, Frequency-tuning for control of parametrically resonant mass sensors, Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films, vol.23, issue.4, pp.841-845, 2005.
DOI : 10.1116/1.1924717

I. H. Hassan, The asymptotic expansion and numerical verification method for linear and nonlinear initial value problem, Applied Mathematics and Computation, vol.180, issue.1, pp.29-37, 2006.
DOI : 10.1016/j.amc.2005.11.146

B. Abdo, E. Segev, O. Shtempluck, and E. Buks, Unusual nonlinear dynamics observed in NbN superconducting microwave resonators, Institute of Physics Publishing, Conference Series, 7 th European Conference on Applied Superconductivity, pp.1346-1349, 2006.

R. Aguilar-lópez and R. Martínez-guerra, Chaos suppression via observer based active control scheme: Application to Duffing???s oscillator, Chaos, Solitons & Fractals, vol.32, issue.5, pp.1887-1897, 2007.
DOI : 10.1016/j.chaos.2005.12.012

S. Ai and S. P. Hastings, A shooting approach to layers and chaos in a forced duffing equation, arXiv :math.DS/0105043v1, pp.2001-2002, 2001.

R. Almog, S. Zaitsev, O. Shtempluck, and E. Buks, Signal amplification in a nanomechanical duffing resonator via stochastic resonance, arXiv :cond-mat, 2006.

G. Alvarez-marañón, L. Hernández-encinas, F. M. Vitini, and J. M. Masqué, Cryptanalysis of anovel cryptosystem based on chaotic oscillators and feedback inversion, 2003.

P. Amore and A. Aranda, Presenting a new method for the solution of nonlinear problems, arXiv :math-ph, 2003.

P. Amore and A. Raya, Comparison of alternative improved perturbative methods for nonlinear oscillations, arXiv :math-ph, 2004.

H. N. Arafat and A. H. Nayfeh, Non-linear responses of suspended cables to primary resonance excitations, Journal of Sound and Vibration, vol.266, issue.2, pp.325-354, 2003.
DOI : 10.1016/S0022-460X(02)01393-7

R. L. Badzey, G. Zolfagharkhani, A. Gaidarzhy, and P. Mohanty, A controllable nanomechanical memory element, Applied Physics Letters, vol.85, issue.16, 2004.
DOI : 10.1063/1.1808507
URL : http://arxiv.org/abs/cond-mat/0503258

G. K. Bergey and P. J. Franaszczuk, Epileptic seizures are characterized by changing signal complexity, Clinical Neurophysiology, vol.112, issue.2
DOI : 10.1016/S1388-2457(00)00543-5
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.32.7975

E. Buks and M. L. Roukes, Metastability and the Casimir effect in micromechanical systems, Europhysics Letters (EPL), vol.54, issue.2, pp.220-226, 2001.
DOI : 10.1209/epl/i2001-00298-x

E. Buks and B. Yurke, Dephasing due to intermode coupling in superconducting stripline resonators, arXiv :quant-ph, 2005.
DOI : 10.1103/physreva.73.023815
URL : http://arxiv.org/abs/quant-ph/0511033

H. Cao, J. M. Seoane, and M. A. Sanjuán, Symmetry-breaking analysis for the general Helmholtz???Duffing oscillator, Chaos, Solitons & Fractals, vol.34, issue.2, pp.1-16, 2006.
DOI : 10.1016/j.chaos.2006.04.010

H. B. Chan, V. A. Aksyuk, R. N. Kleiman, D. J. Bishop, and F. Capasso, Nonlinear micromechanical casimir oscillator, arXiv :quant-ph, 2001.
DOI : 10.1103/physrevlett.87.211801
URL : http://arxiv.org/abs/quant-ph/0109046

V. K. Chandrasekar, S. N. Pandey, M. Senthilvelan, and M. Lakshmanan, A simple and unified approach to identify integrable nonlinear oscillators and systems, arXiv :nlin, 2005.

V. Chua, Cubic-quintic duffing oscillators, 2003.

A. N. Cleland and M. L. Roukes, A nanometre-scale mechanical electrometer, Nature, vol.276, issue.6672, pp.160-162, 1998.
DOI : 10.1038/32373

W. O. Davis, O. M. O-'reilly, and A. P. Pisano, On the Nonlinear Dynamics of Tether Suspensions for MEMS, Journal of Vibration and Acoustics, vol.126, issue.3, pp.326-331, 2004.
DOI : 10.1115/1.1760558

C. Depassier and B. Rafael, Variational calculation of the period of nonlinear oscillators, 2004.

M. C. Depassier and J. Mura, Variational approach to a class of nonlinear oscillators with several limit cycles, arXiv :nlin.CD, 2001.

J. F. Dunne and P. Hayward, A split-frequency harmonic balance method for nonlinear oscillators with multi-harmonic forcing, Journal of Sound and Vibration, vol.295, issue.3-5, pp.939-963, 2006.
DOI : 10.1016/j.jsv.2006.01.050

H. G. Enjieu-kadji and R. Yamapi, General synchronization dynamics of coupled Van der Pol???Duffing oscillators, Physica A: Statistical Mechanics and its Applications, vol.370, issue.2, pp.316-328, 2006.
DOI : 10.1016/j.physa.2006.03.013

D. Ghosh, A. R. Chowdhury, and P. Saha, On the various kinds of synchronization in delayed Duffing-Van der Pol system, Communications in Nonlinear Science and Numerical Simulation, vol.13, issue.4, pp.1-14, 2006.
DOI : 10.1016/j.cnsns.2006.07.001

A. M. Harb, A. A. Zaher, A. A. Qaisia, and M. A. Zohdy, Recursive backstepping control of chaotic Duffing oscillators, Chaos, Solitons & Fractals, vol.34, issue.2, pp.1-7, 2006.
DOI : 10.1016/j.chaos.2006.03.119

]. C. Heneghan, S. M. Khanna, A. Flock, M. Ulfendahl, L. Brundin et al., Investigating the nonlinear dynamics of cellular motion in the inner ear using the short-time Fourier and continuous wavelet transforms, IEEE Transactions on Signal Processing, vol.42, issue.12, pp.3335-3352, 1994.
DOI : 10.1109/78.340771

H. Hu, Solutions of the Duffing-harmonic oscillator by an iteration procedure, Journal of Sound and Vibration, vol.298, issue.1-2, pp.446-452, 2006.
DOI : 10.1016/j.jsv.2006.05.023

X. M. Huang, Ultrahigh and microwave frequency nanomechanical systems, 2004.
DOI : 10.1088/1367-2630/7/1/247
URL : http://doi.org/10.1088/1367-2630/7/1/247

X. M. Huang, X. L. Feng, C. A. Zorman, M. Mehregany, and M. L. , Roukes, VHF, UHF and microwave frequency nanomechanical resonators, New Journal of Physics, vol.7, issue.247, pp.1-15, 2005.
DOI : 10.1088/1367-2630/7/1/247
URL : http://doi.org/10.1088/1367-2630/7/1/247

L. Ingber, R. Srinivasan, and P. L. Nunez, Path-integral evolution of chaos embedded in noise: Duffing neocortical analog, Mathematical and Computer Modelling, vol.23, issue.3, 2000.
DOI : 10.1016/0895-7177(95)00232-4

J. C. Ji, Nonresonant Hopf bifurcations of a controlled van der Pol???Duffing oscillator, Journal of Sound and Vibration, vol.297, issue.1-2, pp.183-199, 2006.
DOI : 10.1016/j.jsv.2006.03.043

K. Josi and S. Peles, Synchronization in networks of general, weakly nonlinear oscillators, Journal of Physics A: Mathematical and General, vol.37, issue.49, pp.11801-11817, 2004.
DOI : 10.1088/0305-4470/37/49/004

I. Katz, A. Retzker, R. Straub, and R. Lifshitz, Classical to quantum transition of a driven nonlinear nanomechanical resonator, arXiv :cond-mat, pp.1-9, 2007.

B. E. Keen and W. H. Fletcher, Nonlinear plasma instability effects for subharmonic and harmonic forcing oscillations, Journal of Physics A: General Physics, vol.5, issue.1, pp.152-165, 1972.
DOI : 10.1088/0305-4470/5/1/020

I. Kovacic, Adiabatic invariants of oscillators with one degree of freedom, Journal of Sound and Vibration, vol.300, issue.3-5, pp.695-708, 2007.
DOI : 10.1016/j.jsv.2006.08.036

H. Krömmer, A. Erbe, A. Tilke, S. Manus, and R. H. Blick, Nanomechanical resonators operating as charge detectors in the nonlinear regime, Europhysics Letters (EPL), vol.50, issue.1, pp.101-106, 2000.
DOI : 10.1209/epl/i2000-00241-3

A. P. Kuznetsov and J. V. Sedova, On features of scaling in Duffing oscillator under action of impulses with random modulation of parameters, p.611040, 2006.

W. Lacarbonara, H. N. Arafat, and A. H. Nayfeh, Non-linear interactions in imperfect beams at veering, International Journal of Non-Linear Mechanics, vol.40, issue.7, pp.987-1003, 2005.
DOI : 10.1016/j.ijnonlinmec.2004.10.006

S. A. Lazzouniabb, M. Siewe-siewe, F. M. Kakmeni, and S. Bowong, Slow flow solutions and chaos control in an electromagnetic seismometer system, Chaos, Solitons & Fractals, vol.29, issue.4, pp.988-1001, 2006.
DOI : 10.1016/j.chaos.2005.08.061

J. C. Lee, W. D. Oliver, K. K. Berggren, and T. P. Orlando, Nonlinear resonant behavior of the dispersive readout scheme for a superconducting flux qubit, arXiv :cond-mat, 2006.

C. W. Lim, B. S. Wu, and W. P. Su, Higher accuracy analytical approximations to the Duffing-harmonic oscillator, Journal of Sound and Vibration, vol.296, issue.4-5, pp.1039-1045, 2006.
DOI : 10.1016/j.jsv.2006.02.020

J. Liu, D. T. Martin, K. Kadirvel, T. Nishida, M. Sheplak et al., Nonlinear identificaiton of a capacitive dual-backplate MEMS microphone, International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2005.

L. Liu, J. P. Thomas, E. H. Dowell, P. Attar, and K. C. Hall, A comparison of classical and high dimensional harmonic balance approaches for a Duffing oscillator, Journal of Computational Physics, vol.215, issue.1, pp.298-320, 2006.
DOI : 10.1016/j.jcp.2005.10.026

P. Malatkar, Nonlinear vibrations of cantilever beams and plates, 2003.

P. Malatkar and A. H. Nayfeh, CALCULATION OF THE JUMP FREQUENCIES IN THE RESPONSE OF s.d.o.f. NON-LINEAR SYSTEMS, Journal of Sound and Vibration, vol.254, issue.5, pp.1005-1011, 2002.
DOI : 10.1006/jsvi.2001.4104

V. B. Mandelzweig and F. Tabakin, Quasilinearization approach to nonlinear problems in physics with application to nonlinear odes, arXiv :physics, 2001.

V. Marinca and N. Heri¸sanuheri¸sanu, Periodic solutions of duffing equation with strong nonlinearity, Chaos, Solitons and Fractals, pp.1-6, 2006.

C. Mayol, R. Toral, and C. R. Mirasso, On the derivation of amplitude equations for nonlinear oscillators subject to arbitrary forcing, arXiv :cond-mat, 2003.

F. M. Moukam-kakmeni, S. Bowong, C. Tchawoua, and E. Kaptouom, Dynamics and chaos control in nonlinear electrostatic transducers, Chaos, Solitons & Fractals, vol.21, issue.5, pp.1093-1108, 2004.
DOI : 10.1016/j.chaos.2003.12.087

B. Mudavahhu, Singular perturbation techniques, the multiple scales, averaging, renormalization group and invariante condition methods, 2000.

O. Narayan and J. Roychowdhury, Analyzing oscillators using multitime PDEs, IEEE Transactions on circuits and systems I : Fundamental theory and applications 58, pp.894-903, 2003.
DOI : 10.1109/tcsi.2003.813976
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.75.4082

A. Hasan and N. , Resolving controversies in the application of the method of multiples sacles and the generalized method of averaging, Nonlinear Dynamics, vol.40, pp.61-102, 2005.

M. Pandey, K. Aubin, M. Zalalutdinov, R. B. Reichenbach, A. T. Zehnder et al., Analysis of Frequency Locking in Optically Driven MEMS Resonators, Journal of Microelectromechanical Systems, vol.15, issue.6, pp.1546-1554, 2006.
DOI : 10.1109/JMEMS.2006.879693

S. J. Papadakis, A. R. Hall, P. A. Williams, L. Vicci, M. R. Falvo et al., Resonant Oscillators with Carbon-Nanotube Torsion Springs, Physical Review Letters, vol.93, issue.14, pp.146101-146105, 2004.
DOI : 10.1103/PhysRevLett.93.146101

A. Pelster, H. Kleinert, and M. Schanz, High-order variational calculation for the frequency of time-periodic solutions, arXiv :math-ph, 2002.

L. Peng, Existence and uniqueness of periodic solutions for a kind of Duffing equation with two deviating arguments, Mathematical and Computer Modelling, vol.45, issue.3-4, pp.378-386, 2007.
DOI : 10.1016/j.mcm.2006.05.012

N. Alexander, R. Pisarchik, and . Jaimes-reategui, Intermittent lag synchronization in a nonautonomous system of coupled oscillators, Physics Letters A, vol.338, pp.141-149, 2005.

A. Posta and W. Stuiver, Modeling non-linear oscillators: a new approach, International Journal of Non-Linear Mechanics, vol.39, issue.6, pp.897-908, 2004.
DOI : 10.1016/S0020-7462(03)00073-8

R. B. Reichenbach, M. Zalalutdino, K. L. Aubin, R. Rand, B. H. Houston et al., Third-order intermodulation in a micromechanical thermal mixer, Journal of Microelectromechanical Systems, vol.14, issue.6, pp.1244-1245, 2005.
DOI : 10.1109/JMEMS.2005.859080

T. Risler, J. Prost, and F. Julicher, Universal critical behaviorof noisy coupled oscillators, arXiv :cond-mat, 2004.
DOI : 10.1103/physrevlett.93.175702
URL : http://arxiv.org/abs/cond-mat/0409468

D. H. Santamore, H. S. Goan, G. J. Milburn, and M. L. Roukes, Anharmonic effects on a phonon number measurement of a quantum mesoscopic mechanical oscillator, arXiv :quant-ph, 2004.

V. Sazonova, Y. Yaish, H. Ustunel, D. Roundy, T. A. Arias et al., A tunable carbon nanotube electromechanical oscillator, Nature, vol.285, issue.7006, pp.284-287, 2004.
DOI : 10.1063/1.1418256
URL : http://arxiv.org/abs/cond-mat/0409407

G. Sebald, L. Lebrun, and D. Guyomar, Modeling of elastic nonlinearities in ferroelectric materials including nonlinear losses: application to nonlinear resonance mode of relaxors single crystals, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.52, issue.4, pp.52-596, 2005.
DOI : 10.1109/TUFFC.2005.1428042

A. D. Speliotopoulos, The general structure of eigenvalues in nonlinear oscillators, Journal of Physics A: Mathematical and General, vol.33, issue.20, pp.3809-3823, 2000.
DOI : 10.1088/0305-4470/33/20/307

C. Stambaugh and H. B. Chan, Noise activated switching ina driven, nonlinear micromechanical oscillator, arXiv :cond-mat, 2005.
DOI : 10.1103/physrevb.73.172302
URL : http://arxiv.org/abs/cond-mat/0504791

H. Tang, X. M. Huang, M. L. Roukes, M. Bichler, and W. Wegscheider, Two-dimensional electron-gas actuation and transduction for GaAs nanoelectromechanical systems, Applied Physics Letters, vol.81, issue.20, pp.3879-3881, 2002.
DOI : 10.1063/1.1516237
URL : http://authors.library.caltech.edu/3272/1/TANapl02.pdf

G. Wang and S. He, A quantitative study on detection and estimation of weak signals by using chaotic duffing oscillators, IEEE Transactions Fundamental Theory and Applications, vol.50, issue.1 7, pp.945-953, 2003.

W. H. Warner and P. R. Sethna, A generalization of the theory of normal forms, arXiv :chao-dyn, 1995.

Y. Weissman, A contribution to the theory and practice of multiple time scales expansion of nonlinear oscillators, Journal of Physics A: Mathematical and General, vol.12, issue.10, pp.1699-1709, 1979.
DOI : 10.1088/0305-4470/12/10/016

P. Woafo, R. Yamapi, and J. B. Orou, Dynamics of a nonlinear electromechanical system with multiple functions in series, Communications in Nonlinear Science and Numerical Simulation, vol.10, issue.3, pp.229-251, 2005.
DOI : 10.1016/j.cnsns.2003.09.002

B. S. Wu, W. P. Sun, and C. W. Lim, An analytical approximate technique for a class of strongly non-linear oscillators, International Journal of Non-Linear Mechanics, vol.41, issue.6-7, pp.766-774, 2006.
DOI : 10.1016/j.ijnonlinmec.2006.01.006

X. Yang, W. Xu, Z. Sun, and Y. P. Xu, Responses of strongly non-linear oscillator parametrically excited by random narrow-band noise, Applied Mathematics and Computation, vol.171, issue.2, pp.885-899, 2005.
DOI : 10.1016/j.amc.2005.01.096

S. Zaitsev, R. Almog, O. Shtempluck, and E. Buks, Nonlinear Dynamics in Nanomechanical Oscillators, 2005 International Conference on MEMS,NANO and Smart Systems, 2005.
DOI : 10.1109/ICMENS.2005.88
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.608.5357

W. Zhang and K. L. Turner, Nonlinear dynamics of micro impact oscillators in high frequency mems switch application, Transducers The 13th international conference on solid-state sensors and actuators, 2005.

W. Zhang and B. R. Xiang, A Duffing oscillator algorithm to detect the weak chromatographic signal, Analytica Chimica Acta, vol.585, issue.1, pp.1-5, 2007.
DOI : 10.1016/j.aca.2006.12.020